Two Proportions: Videos & Practice Problems

An analyst plans to compare the proportion of smartphone users aged $18\text{–}29$ and $50\text{–}64$ who use a particular app. Prior pilot data suggest that ${\hat{p}}_1=0.30$ for the younger group and ${\hat{p}}_2=0.50$ for the older group. She wants the margin of error for the difference to be within $5$ percentage points with $90\%$ confidence and will sample both groups equally. What total sample size should she collect?